Adjacency-based, non-intrusive model reduction for vortex-induced vibrations

Abstract

Vortex-induced Vibrations (VIV) pose computationally expensive problems of high practical interest to several engineering fields. In this work we develop a non-intrusive, reduced-order modeling methodology, applied to two-dimensional (2D), VIV cases subject to a laminar, incompressible flow. Performing a physics-informed approximation of the Arbitrary Lagrangian–Eulerian (ALE) incompressible Navier–Stokes (NS), we derive a discrete-time, quadratic-bilinear model structure for the velocity flowfield on a reference domain. This structure, along with a predefined sparsity pattern motivated by the adjacency-based sparsity of the discretized NS-ALE operators, leads to the formulation of a sparse, full-order model (sFOM) inference problem. Thus, the data-driven inference task requires solving many “local” least squares (LS) problems, isolating the contribution of geometrically “nearest neighbours” for each degree of freedom. Numerical aspects of inference such as data centering and regularization, as well as the direct enforcement of boundary conditions under the sFOM formulation are extensively discussed. The inferred, sFOM operators are then projected to a non-intrusive reduced-order model (ROM) for the velocity flowfield via the Proper Orthogonal Decomposition (POD). The resulting non-intrusive ROM (sFOM-POD) is coupled with the first-principle, 2D solid oscillation equations, resulting to a hybrid physics-informed/first-principle VIV dynamics model, simulated using an implicit time integration scheme. The mapping of the coupled solution from the ALE reference domain to the current configuration is also presented. This methodology is applied to two testcases of an elliptical, non-deformable solid mounted on springs, subject to Re=90,180 flows. Numerical results indicate a successful coupling between the data-driven flowfield and solid dynamics, with prediction errors of less than 3% for both the flowfield and the solid oscillation. A comparative study with respect to the sFOM-POD dimension indicates the robustness and potential of the approach.